On the Volterra integral equation with weakly singular kernel

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2006 Latin Publisher:Institute of Mathematics, Czech Academy of SciencesJournal:Mathematica Bohemica, volume 131, pages 225-231 (issn: 0862-7959, eissn: 2464-7136,

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Authors: Szufla, Stanisław;

doi: 10.21136/mb.2006.134139

On the Volterra integral equation with weakly singular kernel

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Abstract

Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.

Keywords

Singular nonlinear integral equations, measure of noncompactness, integrable solution

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